Semiconductor manufacturing technology now requires the formation of nanoscale features on semiconductor substrates. Due to the ever-increasing levels of miniaturization, fabrication technologies are needed that are capable of forming intricate design patterns within ever-decreasing areas. There are various nanoscale fabrication technologies currently in use. For instance, one type of nanoscale fabrication technology is immersion optical and interference lithography. Unfortunately, it has become more and more difficult to focus light at sub-20-nanometer (nm) scales, and thus the resolution of immersion optical and interference lithography is limited. Scanning electron beam lithography is also used in nanoscale fabrication. However, scanning electron beam lithography does not have a high enough throughput to satisfy current industrial mass-production demands.
Self-assembling materials, such as block copolymers, are another promising candidate for nanoscale fabrication. These self-assembling materials are capable of self-assembly into nanoscale structures. To do this, topographical features are formed on a template region, which orients the self-assembly of the self-assembling materials in a desired manner. This thus alleviates the fabrication demands on other types of nanoscale fabrication technologies. In other words, these other types of fabrication technologies simply need to create the topographical features, and do not have to precisely form each of the intricate features of a nanoscale pattern. Instead, the topographical features are formed in the template region, which orients the self-assembly of the self-assembling materials, resulting in a desired nanoscale pattern. Unfortunately, these topographical configurations are determined ad hoc. Currently, determining the topographical configurations that result in desired nanoscale patterns is simply done by trial and error. This is a significant practical limitation, given that an almost unlimited number of nanoscale patterns will be required by semiconductor manufacturers. As such, more methodological techniques are needed to determine topographical configurations for self-assembly.